System and method for crest factor reduction

ABSTRACT

A crest reduction system and method. The inventive system includes a first circuit for suppressing peak amplitudes of an input signal and providing a peak amplitude suppressed signal in response thereto and a second circuit coupled to the first circuit for rejecting intermodulation distortion in the amplitude suppressed signal. In the illustrative implementation, the first circuit is a peak amplitude suppressor having circuitry for computing an amplitude of the input signal and for computing a gain factor for the input signal in response thereto. In the best mode, the gain factor is obtained from a lookup table. The peak amplitude suppressor further includes a multiplier for applying the gain factor to the input signal. In the illustrative embodiment, the second circuit includes a plurality of bandpass filters and a summer for combining the outputs thereof.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.60/616,716, filed Oct. 7, 2004, the disclosure of which is incorporatedherein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to electrical and electronic circuits andsystems. More specifically, the present invention relates to systems andmethods for reducing crest factor in electrical and electronic circuitsand systems.

2. Description of the Related Art

In Multi-Carrier Power Amplifier (MCPA) communication transmissionapplications, multiple carriers are typically combined in the baseband,intermediate frequency (IF) or radio frequency (RF) frequency range andthe resulting signal is transmitted using a single power amplifier. Anobjective for MCPA transmission is to transmit a signal at a very highefficiency while maintaining a low Adjacent Channel Power Ratio (ACPR)to meet spectral mask requirements. ACPR is defined as the ratio ofpower in a bandwidth away from the main signal (the distortion product)to the power in a bandwidth within the main signal. The bandwidths andlocations are functions of the standards being employed.

To achieve high efficiency power amplifier (PA) transmission, it isdesirable to use semi-non-linear PAs, such as Class A/B PAs. A challengefor MCPA signal transmission is due to the fact that the combined signalhas a high crest factor (ratio of peak power to average power), wherethe peak power is significantly higher than the average power. A smallportion of the combined signal can have very high peaks and whentransmitted at high PA efficiency, these high-level signals reach intothe saturated region of the PA's transfer function and the output of thePA has high intermodulation distortion (IMD). The high IMD level raisesthe ACPR levels.

To maintain low ACPR without any linearization techniques, the transmitsignal level must be decreased sufficiently so that the peak amplitudesare not in the saturated zone of the PA, but this reduces the amplifierefficiency. For example, a four carrier W-CDMA (wideband code divisionmultiple access) signal can have a crest factor exceeding 13 dB. If thecrest factor is reduced by about 6 dB, the average power can beincreased by 6 dB thus increasing the power efficiency by a factor of 4.

One conventional approach to this problem is to limit the amplitude ofeither the baseband signal or the RF signal output of each channel usinga look-ahead approach. However, it is difficult to generate signals withlow crest factor and low ACPR inasmuch as limiting the amplitudeincreases out of band emissions (e.g. sidelobes) and thereby raises theACPR level. While, efforts to reduce the ACPR levels generally increasecrest factor.

Another prior approach involves the use of unused CDMA codes to reducethe crest factor in the output signals. However, this approach requiresknowledge of what is being transmitted so that the unused codes can beidentified. This adds to the complexity, storage requirements and costof the system.

Hence, a need remains in the art for an improved system or method forreducing the crest factor in communications systems while maintaining alow ACPR therefor.

SUMMARY OF THE INVENTION

The need in the art is addressed by the crest reduction system andmethod of the present invention. In a most general embodiment, theinventive system includes a first circuit for suppressing peakamplitudes of an input signal and providing a peak amplitude suppressedsignal in response thereto and a second circuit coupled to the firstcircuit for rejecting intermodulation distortion in the amplitudesuppressed signal.

In the illustrative implementation, the first circuit is a peakamplitude suppressor having circuitry for computing an amplitude of theinput signal and for computing a gain factor for the input signal inresponse thereto. In the best mode, the gain factor is obtained from alookup table. The peak amplitude suppressor further includes amultiplier for applying the gain factor to the input signal.

In the illustrative embodiment, the second circuit includes a pluralityof bandpass filters and a summer for combining the outputs thereof. Asan alternative, the second circuit is implemented with a plurality offinite impulse response (FIR) filters. The outputs of the FIR filtersare Fast Fourier Transformed and predetermined bands of the output ofthe FFT are selected and combined to provide a crest factor reducedoutput signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified block diagram of an illustrative implementationof a system for crest factor reduction in accordance with the teachingsof the present invention;

FIG. 2 is a simplified block diagram showing an illustrativeimplementation of the peak amplitude suppressor of the crest reductionsystem of the present invention;

FIG. 3 is a series of graphs that illustrate the operation of thepresent invention. FIG. 3(A) shows the typical output of an amplitudesuppressor;

FIG. 3(B) shows an illustrative passband of the intermodulation rejectfilter of FIG. 1;

FIG. 3(C) shows an illustrative output of the intermodulation rejectfilter of FIG. 1;

FIG. 4 is a simplified block diagram of an illustrative implementationof the IMD reject filter of FIG. 1;

FIG. 5(A) shows the spectrum shape of the input of the alternativeembodiment of the IMD reject filter, which contains the desired signalsto be transmitted and the IMD components that are generated by the peakamplitude suppressor;

FIG. 5(B) shows signal bands D₁, D₂, . . . D_(N) corresponding to IMDsignals;

FIG. 5(C) shows the resulting spectrum of the output signal after theoutput of the amplitude suppressor is passed though the filter of FIG.6;

FIG. 6 shows an alternative embodiment of the IMD reject filter of FIG.1;

FIG. 7 is a simplified block diagram of an alternative illustrativepolyphase implementation of the IMD reject filter in accordance with thepresent teachings;

FIG. 8 is a series of graphs designed to illustrate the operation of thefilter of FIG. 7;

FIG. 9 is a simplified block diagram of an alternative illustrativepolyphase implementation of the IMD reject filter in accordance with thepresent teachings;

FIG. 10 is a series of graphs designed to illustrate the operation ofthe filter of FIG. 9;

FIG. 11 illustrates passbands filtering in accordance with the presentteachings;

FIG. 12 illustrates notchbands filtering in accordance with the presentteachings;

FIG. 13 is an illustrative implementation of a single Multi bands andArbitrary Shape Filter that support multiple bandpass signals for evenlength filter; and

FIG. 14 is an illustrative implementation of a single Multi bands andArbitrary Shape Filter that support multiple bandpass signals for oddlength filter.

DESCRIPTION OF THE INVENTION

Illustrative embodiments and exemplary applications will now bedescribed with reference to the accompanying drawings to disclose theadvantageous teachings of the present invention.

While the present invention is described herein with reference toillustrative embodiments for particular applications, it should beunderstood that the invention is not limited thereto. Those havingordinary skill in the art and access to the teachings provided hereinwill recognize additional modifications, applications, and embodimentswithin the scope thereof and additional fields in which the presentinvention would be of significant utility.

FIG. 1 is a simplified block diagram of an illustrative implementationof a system for crest factor reduction in accordance with the teachingsof the present invention. The system 10 includes a peak amplitudesuppressor 20 and an intermodulation rejection filter 30. A baseband, IFor RF input signal may be expressed as:X ₁(n)=I ₁(n)+jQ ₁(n)  [1]The signal X(n) is amplitude clipped by the suppressor 20. The phase ismaintained to minimize the signal distortion in the following manner:X(n)=X(n) if A(n)<T  [2]X(n)=X(n)T/A(n); if A(n)≧T  [3]where A(n)=|X(n)| is the instantaneous amplitude of the signal X(n), andT is the amplitude threshold of the clipping.

FIG. 2 is a simplified block diagram showing an illustrativeimplementation of the peak amplitude suppressor of the crest reductionsystem of the present invention. The in-phase and quadrature componentsof the input are used to compute the amplitude via an amplitude detector22. In practice, the amplitude detector 22 may be implemented withcordic I/Q to amplitude processing.

The detected amplitude is then fed to a gain factor generator 24. In thebest mode, the gain factor generator 24 is implemented with a lookuptable (LUT). The LUT 24 stores the T/A(t) gain values. The gain is thenapplied by first and second multipliers 12 and 14, respectively, to theoriginal signal delayed by first and second delayed elements 26 and 28respectively. The delay is used to match the delay amount occurring inthe amplitude and LUT processing so that the gain is applied to theinputs from which it was computed. This process can be applied at IF orRF where the signal amplitude can be estimated via envelope detection.

After processing by the peak amplitude suppressor 20, the amplitude ofthe input signal will have a lower crest factor. However,inter-modulation distortion (IMD) is often generated. This isillustrated in FIG. 3.

FIG. 3 is a series of graphs that illustrate the operation of thepresent invention. FIG. 3(A) shows the typical output of an amplitudesuppressor with the desired signals shown at 33 and IMD shown at 35.FIG. 3(B) shows an illustrative passband 37 of the intermodulationreject filter 30 of FIG. 1. FIG. 3(C) shows an illustrative output ofthe intermodulation reject filter 30 of FIG. 1. To suppress the IMD, thedesired signals filter 30 selects the desired signal band or bands andperforms signal filtering of these bands only: the desired signal bandsare passed while the intermodulation components are attenuated. In thisprocess, the intermodulation products are suppressed with the filtersidelobes, resulting in a high ACPR signal. FIG. 3(A) shows the spectrumshape of the signal input to the Inter-Modulation Reject Filter 30,which contains the desired signals to be transmitted and the IMDcomponents that are generated by the Peak Amplitude Suppressor 20. FIG.3(B) shows the desired signal bands S₁, S₂, . . . , S_(N) correspondingto the desired signal. After passing though a filter with thecharacteristic shown in FIG. 3(B), an output signal is provided with aspectrum illustrated in FIG. 3(C).

In accordance with the present teachings, at least two approaches can beused to suppress IMD. A first approach, as illustrated in FIG. 4, is toselect the desired signal components. A second approach, illustrated inFIGS. 5 and 6 is to reject the undesirable IMD components per se.

FIG. 4 is a simplified block diagram of an illustrative implementationof the IMD reject filter 30 of FIG. 1. In this embodiment, the rejectfilter 30 consists of plural passband filters, e.g. 32, 34 and 36,followed by a summer 44. Each filter 32, 34 and 36 and its associateddelay 38, 40 and 42 can be expressed as a Finite Impulse Response (FIR)filter as follows: $\begin{matrix}{{S_{1}\text{:}h_{S\quad 1}} = {\sum\limits_{k = 0}^{{K\quad 1} - 1}{h_{{S\quad 1},k}z^{- k}}}} & \lbrack 4\rbrack \\{{S_{2}\text{:}\quad h_{S\quad 2}} = {\sum\limits_{k = 0}^{{K\quad 2} - 1}{h_{{S\quad 2},k}z^{- k}}}} & \lbrack 5\rbrack \\{{S_{N}\text{:}\quad h_{SN}} = {\sum\limits_{k = 0}^{{KN} - 1}{h_{{S\quad 1},k}z^{- k}}}} & \lbrack 6\rbrack\end{matrix}$The resulting filter is then expressed as $\begin{matrix}{{S_{1} + S_{2} + \ldots + {S_{N}:h_{S\quad 1}}} = {{\sum\limits_{k = 0}^{{K\quad 1} - 1}{h_{{S\quad 1},k}z^{- k}}} + {\sum\limits_{k = 0}^{{K\quad 2} - 1}{h_{{S\quad 2},k}z^{- k}}} + \ldots + {\sum\limits_{k = 0}^{{KN} - 1}{h_{{SN},k}z^{- k}}}}} & \lbrack 7\rbrack\end{matrix}$which is a single FIR filter. The filter components at each delay can becombined to provide the following filter structure: $\begin{matrix}{{S_{1} + S_{2} + \ldots + {S_{N}:\left\{ h \right\}}} = {\sum\limits_{h = 0}^{\max{({{{K\quad 1} - 1},\quad{{K\quad 2} - 1},\quad\ldots\quad,{{KN} - 1}})}}{h_{k}z^{- h}}}} & \lbrack 8\rbrack\end{matrix}$This implies that the reject filter 30 (S₁+S₂+ . . . +S_(N)) can beimplemented with a single FIR filter.

One way to use this approach is to design a filter for a single carrier,a filter for two adjacent channels, a filter for three adjacentchannels, and a filter for four adjacent channels, etc. For a systemusing equal spaced channel centers, all possible patterns of signals isrealizable by frequency shifting and adding this set of filters. In thebest mode, the filter coefficients are combined and used as one FIRfilter. For two adjacent channels, better performance is achieved whenusing a filter which is flat across both spectrums as opposed to usingtwo filters designed for a single carrier.

As noted above, the filter of FIG. 4 is based on a desired signalsapproach. The alternative rejection approach for the filter 30 isillustrated in FIGS. 5 and 6. Similar to the desired signals filtermethod, the rejection filter 30′ performs the filtering of the IMDcomponents and removes the distortion from the original signal.

In this embodiment, to suppress IMD, the filter 30′ selects the IMDsignal bands and performs signal filtering of these bands only. In thisprocess only the intermodulation products are selected, which areremoved from the input signal so that the desired signal is left intactand the IMD is suppressed. FIG. 5(A) shows the spectrum shape of theinput of the alternative embodiment of the IMD reject filter, whichcontains the desired signals to be transmitted and the IMD componentsthat are generated by the peak amplitude suppressor. FIG. 5(B) showssignal bands D₁, D₂, . . . D_(N) corresponding to the IMD signals. FIG.5(C) shows the resulting spectrum of the output signal after the outputof the amplitude suppressor 20 is passed though the filter 30′ of FIG.6.

FIG. 6 shows an alternative embodiment of the IMD reject filter ofFIG. 1. The rejection filter 30′ includes plural filters of which threeare shown 32′, 34′ . . . 36′. Again, in the best mode, the filtercoefficients are combined and used as one FIR filter. The filters aredesigned to pass the IMD in the reject bands D₁, D₂ . . . D_(M)respectively. The outputs of the filters are delayed by associated delayelements 38′, 40′ . . . 42′ and subtracted from a delayed version of theinput signal by a subtractor 44′. The input signal is delayed by element46′. Those skilled in the art will appreciate that the embodiments ofFIGS. 1, 4 and 6 may be implemented in software in which case thecomponents shown are implemented in process steps.

In any event, each filter and its associated delay can be expressed as aFinite Impulse Response (FIR) filter as follows: $\begin{matrix}{{S_{1}\text{:}\quad h_{S}} = z^{- {kS}}} & \lbrack 9\rbrack \\{{D_{1}\text{:}\quad h_{D\quad 1}} = {\sum\limits_{k = 0}^{{K\quad 1} - 1}{h_{{D\quad 1},k}z^{- k}}}} & \lbrack 10\rbrack \\{{D_{2}\text{:}\quad h_{D\quad 2}} = {\sum\limits_{k = 0}^{{K\quad 2} - 1}{h_{{D\quad 2},k}z^{- k}}}} & \lbrack 11\rbrack \\{{D_{M}\text{:}\quad h_{DM}} = {\sum\limits_{k = 0}^{{KM} - 1}{h_{{D\quad 1},k}z^{- k}}}} & \lbrack 12\rbrack\end{matrix}$The resulting filter is then expressed as $\begin{matrix}{{S + D_{1} + D_{2} + \ldots + {D_{N}\text{:}\quad h_{S\quad 1}}} = {Z^{- {kS}} - {\sum\limits_{k = 10}^{{K\quad 1} - 1}{h_{{D\quad 1},k}z^{- k}}} - {\sum\limits_{k = 0}^{{K\quad 2} - 1}{h_{{D\quad 2},k}z^{- k}}} - \ldots - {\sum\limits_{k = 0}^{{KM} - 1}{h_{{DM},k}z^{- k}}}}} & \lbrack 13\rbrack\end{matrix}$which is a single HR filter. The filter components at each delay can becombined to provide the following filter structure: $\begin{matrix}{{S + D_{1} + D_{2} + \ldots + {D_{N}\text{:}\quad\left\{ h \right\}}} = {\sum\limits_{h = 0}^{\max{({{{K\quad 1} - 1},\quad{{K\quad 2} - 1},\quad\ldots\quad,{{KM} - 1}})}}{h_{k}z^{- h}}}} & \lbrack 14\rbrack\end{matrix}$This implies that the reject (S−D₁−D₂− . . . −D_(M)) can be implementedwith a single FHR filter.

The advantage of this approach is that the filter does not distort thedesired signal. Only the intermodulation products are suppressed.Furthermore, because the power of the intermodulation is substantiallysmall compared to the desired signal, the filter does not change thecrest factor substantially.

In applications where the signals are equally spaced, a polyphaseapproach can be used to either select desired signals or reject IMDproducts.

FIG. 7 is a simplified block diagram of an alternative illustrativepolyphase implementation of the IMD reject filter in accordance with thepresent teachings. This filter rejects IMD products by selecting desiredsignals.

FIG. 8 is a series of graphs designed to illustrate the operation of thefilter 50 of FIG. 7. As per FIGS. 3 and 5 above, the first graph (FIG.8(A)) shows the input to the filter, the second graph (FIG. 8(B)) showsthe characteristic of the filter 50 and the third graph (FIG. 8(C))shows the output of the filter.

In the implementation of FIG. 7, the output of the peak amplitudesuppressor 20 of FIG. 1 is divided into an integer multiple, H, ofequal-sized frequency slots by resampler 52 when doing an H-point FFT inthe polyphase implementation for H=2^(x). For H not a power of two, aDFT can be used. The width of these slots is such that only signalenergy or IMD energy is present in each slot. Each slot is filtered by aFIR filter 54, 56, 58 and 60 to pass the component in that frequencyslot and to reject all other frequency components. Thus, by correctlychoosing frequency slots, B_(h), that contain only signal energy, thesignals S_(n) can be chosen such that the signal I₃+jQ₃ contains onlysignal energy, with the intermodulation components rejected. Thisselection is effected after a Fast Fourier Transform (via FFT 62) by afilter 64. The selected outputs of the filter 64 are then combined viasummer 66.

FIG. 9 is a simplified block diagram of an alternative illustrativepolyphase implementation of the IMD reject filter in accordance with thepresent teachings. This filter rejects IMD products output by the peakamplitude detector. The embodiment of FIG. 9 is similar to that of FIG.7 with the exception that the filters are designed to pass the IMDproducts and the output of the summer 66 is subtracted from a delayedversion of the input signal by a subtractor 68′.

FIG. 10 is a series of graphs designed to illustrate the operation ofthe filter 50′ of FIG. 9. As per FIGS. 3 and 5, the first graph (FIG.9(A)) shows the input to the filter, the second graph (FIG. 9(B)) showsthe characteristic of the filter 50′ and the third graph (FIG. 9(C))shows the output of the filter.

In the polyphase distortion filter approach of FIG. 9, the spectrum,shown in FIG. 10, of the output of the peak amplitude suppressor isdivided into an integer multiple, H, of equal-sized frequency slots.Each slot is filtered to pass the component in that frequency slot andto reject all other frequency components. The width of these slots issuch that only signal energy or IMD energy is present in each slot.Thus, by correctly choosing frequency slots, B_(h), that contain onlyIMD energy, the intermodulation distortion components, D_(n), of FIG. 9can be chosen such that the signal I₃+jQ₃ contains only distortionenergy, with the desired signal components rejected. The final output ofthe filter 52′ is the difference between the input signal I₂+jQ₂,properly delayed, and the sum of signals, D_(n). This signal containsonly signal energy with the distortion removed.

A multibands and arbitrary shape filter can be implemented in passbandsmode where the desired bands are selected and the undesired bands suchas intermodulation distortion (IMD) bands are removed.

FIG. 11 illustrates passbands filtering in accordance with the presentteachings. The objective is to select the desired signal by forming thecombined filtering of these desired signals. FIG. 11(A) shows the inputsignal; FIG. 11(B) shows the spectral characteristic of a passbandfilter; and FIG. 11(C) shows the output filtered signal.

The transmit signal can be a combination of multiple carriers atarbitrary frequencies, and thus the spectrum can be asymmetric. In theseapplications multiple bandpass filters can be designed, follow by afilter combination process to realize the combined filter with a singlefilter. Let I_(i)(n)+jQ_(i)(n) be the input signal of the filter. Theoutput of the filter can be expressed asI _(o)(n)+jQ _(o)(n)={I _(i)(n)+jQ _(i)(n)}*g(n)  [15]where g(n) is the composite filter. We can expand g(n) and rewrite theequation as $\begin{matrix}{{{I_{o}(n)} + {j\quad{Q_{o}(n)}}} = {\left\{ {{I_{i}(n)} + {j\quad{Q_{i}(n)}}} \right\}*\left\{ {{{h_{1}(n)} \cdot {\mathbb{e}}^{j\quad\omega_{1}n}} + {{h_{2}(n)} \cdot {\mathbb{e}}^{{j\omega}_{2}n}} + \ldots + {{h_{N}(n)} \cdot {\mathbb{e}}^{{j\omega}_{N}n}}} \right\}}} & \lbrack 16\rbrack \\{= {\left\{ {{I_{i}(n)} + {j\quad{Q_{i}(n)}}} \right\}*\left\{ {{{{h_{1}(n)} \cdot \cos}\quad\omega_{1}n} + {{{h_{2}(n)} \cdot \cos}\quad\omega_{1}n} + \ldots + {{{h_{N}(n)} \cdot \cos}\quad\omega_{N}n} + {j\left\lbrack {{{{h_{1}(n)} \cdot \sin}\quad\omega_{1}n} + {{{h_{2}(n)} \cdot \sin}\quad\omega_{1}n} + \ldots + {{{h_{N}(n)} \cdot \sin}\quad\omega_{N}n}} \right\rbrack}} \right\}}} & \lbrack 17\rbrack\end{matrix}$where * indicates the convolution process, $\begin{matrix}{{{x(n)}*{y(n)}} = {\sum\limits_{k = 0}^{N - 1}{{x(k)}{{y\left( {n - k} \right)}.}}}} & \lbrack 18\rbrack\end{matrix}$In the above equation, h_(i)(n) is the low pass version of the desiredfilter and Os is the angular frequency of the desired signal. Thefilters h_(i)(n) can have different spectral shapes.

Thus: $\begin{matrix}{{{I_{o}(n)} + {j\quad{Q_{o}(n)}}} = {\left\{ {{I_{i}(n)} + {j\quad{Q_{i}(n)}}} \right\}*{g(n)}}} & \lbrack 19\rbrack \\{{= {\left\{ {{{I_{i}(n)}*{g_{c}(n)}} - {{Q_{i}(n)}*{g_{s}(n)}}} \right\} + {j\left\{ {{{I_{i}(n)}*{g_{s}(n)}} + {{Q_{i}(n)}*{g_{c}(n)}}} \right\}}}}{{where}\text{:}}} & \lbrack 20\rbrack \\{{g(n)} = {{g_{c}(n)} + {j\quad{g_{s}(n)}}}} & \lbrack 21\rbrack\end{matrix}$

Thus:g _(c)(n)=h ₁(n)·cos ω₁ n+h ₂(n)·cos ω₁ n+ . . . +h _(N)(n)·cos ω_(N)n  [22]g _(s)(n)=h ₁(n)·sin ω₁ n+h ₂(n)·sin ω₁ n+ . . . +h _(N)(n)·sin ω_(N)n  [23]

The process is to compute the filter shape h_(i)(n), shift it to thedesired frequency ω_(i), and then combine each in the above fashion toform the single complex filter g(n).

The IMD reject filter can be implemented in notchband mode where theundesired bands (IMD bands) are selected, and the desired bands removed.The resulting filtered signal is then removed from the transmit signalto produce the desired signal that is free from the IMD signals.

FIG. 12 illustrates notchbands filtering in accordance with the presentteachings. The objective is to remove undesired signal components byisolating the undesired components with filters and then removing thosecomponents from the original signal. FIG. 12(A) shows the input signal;FIG. 12(B) shows the spectral characteristic of a notch filter; and FIG.12(C) shows the output-filtered signal.

The transmitted signal can be a combination of multiple carriers atarbitrary frequency locations, and thus the spectrum can be asymmetric.In these applications multiple undesired-band filters can be designed,followed by a filter combination process to realize the combined filterwith a single filter. Let I_(i)(t)+jQ_(i)(t) be the input signal of thefilter. The output of the filter can be expressed asI _(o)(n)+jQ _(o)(n)={I _(i)(n)+jQ _(i)(n)}*h _(passthru)(n)·−{I_(i)(n)+jQ _(i)(n)}*[h ₁(n)·e ^(jω) ¹ ^(n) +h ₂(n)·e ^(ω) ² ^(n) + . . .+h _(N)(n)·e ^(jω) ^(N) ^(n)]  [24]

If we writeI _(o)(n)+jQ _(o)(n)={I _(i)(n)+jQ _(i)(n)}*g(n)  [25]then:g(n)={δ_(k)(n−(N _(taps)+1)/2)−[h ₁(n)·e^(jω) ¹ ^(n) +h ₂(n)·e ^(jω) ²^(n) + . . . +h _(N)(n)·e ^(jω) ^(N) ^(n)]}  [26]where δ_(k)(n−(N_(taps)+1)/2) is the Kronecker delta function with adelay (N_(taps)+1)/2 which represents the group delay of the odd filtertap length N_(taps) of the h's. This length will be the same for allh's.

Expanding,g(n)={δ_(k)(n−(N _(taps)+1)/2)−[h ₁(n)·cos ω₁ n+h ₂(n)·cos ω₂ n+ . . .+h _(N)(n)·cos ω_(N) n]−j[h ₁(n)·sin ω₁ n+h ₂(n)·sin ω₂ N+ . . . +h_(N)(n)·sin ω_(N) n]}tm [27]andI _(o)(n)+jQ _(o)(n)={I _(i)(n)*[δ_(k)(n−(N _(taps)+1)/2)−[h ₁(n)·cos ω₁n+h ₂(n)·cos ω₂ n+ . . . +h _(N)(n)·cos ω_(N) n]]+Q _(i)(n)*[h ₁(n)·sinω₁ n+h ₂(n)·sin ω₂ n+ . . . +h _(N)(n)·sin ω_(N) n]}−j{I _(i)(n)*[h₁(n)·sin ω₁ n+h ₂(n)·sin ω₂ n+ . . . +h _(N)(n)·sin ω_(N) n]−Q_(i)(n)*[δ_(k)(n−(N _(taps)+1)/2)−[h ₁(n)·cos ω₁ n+h ₂(n)·cos ω₂ n+ . .. +h _(N)(n)·cos ω_(N) n]]}  [28]where h_(i)(n) is the lowpass version of the i^(th) undesired-bandfilter, and ω_(i) is the angular frequency of the undesired signal. Thefilters h_(i)(n) can have different spectral shapes.

Thus: $\begin{matrix}{{{I_{o}(n)} + {j\quad{Q_{o}(n)}}} = {\left\{ {{I_{i}(n)} + {j\quad{Q_{i}(n)}}} \right\}*{g(n)}}} & \lbrack 29\rbrack \\{{= {\left\{ {{{I_{i}(n)}*{g_{c}(n)}} - {{Q_{i}(n)}*{g_{s}(n)}}} \right\} + {j\left\{ {{{I_{i}(n)}*{g_{s}(n)}} + {{Q_{i}(n)}*{g_{c}(n)}}} \right\}}}}{{where}\text{:}}} & \lbrack 30\rbrack \\{{g(n)} = {{g_{c}(n)} + {j\quad{g_{s}(n)}}}} & \lbrack 31\rbrack\end{matrix}$

Thusg _(c)(n)=δ_(k)(n−(N _(taps)+1)//2)−[h ₁(n)·cos ω₁ n+h ₂(n)·cos ω₁ n+ .. . +h _(N)(n)·cos ω_(N) n]  [32]g _(s)(n)=−[h ₁(n)·sin ω₁ n+h ₂(n)·sin ω₁ n+ . . . +h _(N)(n)·sin ω_(N)n]  [33]

The process is to compute the filter shape h_(i)(n), shift to thedesired frequency ω_(i), and then combine each in the above fashion toform the single complex filter, g(n).

To design a combination FIR, a passband filtering approach or notchfiltering approach may be used. An illustrative passband filteringapproach is as follows:

-   -   (1) Determine the number of passband filters, M, based on the        desired spectral shape,    -   (2) Design the baseband version of the filters. Each filter will        require N_(m) taps, m=1:M,    -   (3) Select the largest number of taps, i.e., N_(max)=Max(N₁, N₂,        N₃, . . . N_(M)),    -   Redesign the filters with maximum number of taps, to obtain the        coefficients {h_(m)(n)} where m=1:M, n=0:N−1. Since the filters        are at baseband, the coefficients are symmetric.    -   (5) Translate the baseband filter into an WF filter by frequency        shifting. That is:        {w _(m)(n)}={h _(m)(n)e ^(j*2*pi*fn(n))}, m=1:M.  [34]    -   (6) Combine the coefficients of {w_(m)(n)} to form the combine        filter coefficients: $\begin{matrix}        {{\left\{ {g(n)} \right\} = {\sum\limits_{m = 1}^{M}{w_{m}(n)}}},{n = {{0\text{:}N} - 1.}}} & \lbrack 35\rbrack        \end{matrix}$

This filter selects the passband of the desired signal. In matrix form,the filter weights are computed as: $\begin{matrix}\begin{matrix}{\left\lbrack {g\quad(0)\quad g\quad(1)\quad\ldots\quad g\quad\left( {N - 1} \right)} \right\rbrack = \left\lbrack {k_{1}\quad k_{2}\quad\ldots\quad k_{M}} \right\rbrack} \\{\begin{bmatrix}{w_{1}(0)} & {w_{1}(1)} & \ldots & {w_{1}\left( {N - 1} \right)} \\{w_{2}(0)} & {w_{2}(1)} & \ldots & {w_{2}\left( {N - 1} \right)} \\\ldots & \ldots & \ldots & \ldots \\{w_{M}(0)} & {w_{M}(1)} & \ldots & {w_{M}\left( {N - 1} \right)}\end{bmatrix}}\end{matrix} & \lbrack 36\rbrack\end{matrix}$where k_(p) is the weight associated with p^(th) filter, andw_(p)(0:N−1) are the coefficients of the p^(th) filter.

-   -   (7) Build a single complex FIR with N_(max) taps.        For the notch filtering approach, the process is as follows:    -   (1) Determine the number of notch filters, M, based on the        desired spectral shape,    -   (2) Design the baseband version of the notch filters, each        filter will require N_(m) taps, m=1:M,    -   (3) Select the largest number of taps, i.e., N_(max)=Max(N₁, N₂,        N₃, . . . N_(M)), such as N_(max) is odd.    -   (4) Redesign the filters with maximum number of taps, to obtain        the coefficients {h_(m)(n)} where m=1:M, n=0:N−1. Since the        filters are at baseband, the coefficients are symmetric.    -   (5) Translate the baseband filter into IF filter by frequency        shifting, that is        {w _(m)(n)}={h _(m)(n)e ^(j*2*pi*fn(n))}, m=1:M.  [37]    -   (6) Combine the coefficient of {w_(n)(m)} to form the combine        filter coefficients: $\begin{matrix}        {{\left\{ {g(n)} \right\} = {{\delta_{k}\left( {n - {\left( {N_{\max} + 1} \right)/2}} \right)} - {\sum\limits_{m = 1}^{M}{k_{m}{w_{m}(n)}}}}},{n = {{0\text{:}N} - 1.}}} & \lbrack 38\rbrack        \end{matrix}$        This filter removes the notch bands from the original signal.        Notes that z^(−(Nmax+1)/2) represents the delay of the original        signal. In matrix form, the filter weight is computed as:        $\begin{matrix}        {\left\lbrack {{g(0)}\quad{g(1)}\quad\ldots\quad{g\left( {N - 1} \right)}} \right\rbrack = {\left\lbrack {1\quad - {k_{1}\quad\ldots}\quad - k_{M}} \right\rbrack{\quad\begin{bmatrix}        0 & 0 & 1 & 0 & 0 \\        {w_{1}(0)} & {w_{1}(1)} & {w_{1}\left( \frac{N + 1}{2} \right)} & \ldots & {w_{1}\left( {N - 1} \right)} \\        \ldots & \ldots & \ldots & \ldots & \ldots \\        {w_{M}(0)} & {w_{M}(1)} & {w_{M}\left( \frac{N + 1}{2} \right)} & \ldots & {w_{M}\left( {N - 1} \right)}        \end{bmatrix}}}} & \lbrack 39\rbrack        \end{matrix}$        where k_(p) is the weight associated with p^(th) filter, and        w_(p)(0:N−1) are the coefficients of the p^(th) filter.    -   (7) Build a single complex FIR with N_(max) taps.        The Multi bands and Arbitrary Shape Filter structure is as shown        in FIG. 13. The input signal I_(i)(n)+jQ_(i)(n) passes through a        tap delay line of length N (=N_(max)), selected to support the        filter h_(i)(n) spectral requirements.        By careful manipulation of the following equation, the        coefficients, g_(c)(n) and g_(s)(n) can be forced to be        symmetric and anti-symmetric. In the equation,        I _(o)(n)+jQ _(o)(n)={I _(i)(n)+jQ _(i)(n)}*{h ₁(n)·e ^(jω) ¹        ^(n) h ₂(n)·e ^(jω) ² ^(n) + . . . +h _(N)(n)·e ^(jω) ^(N) ^(n)}        we can write each of the modulated filter coefficient terms as        w _(m)(n)=h _(m)(n)·e ^(jω) ^(m) ^(n) =h _(m)(0)e ^(jω) ^(m) ⁰        ,h _(m)(1)e ^(jω) ^(m) ¹ ,h _(m)(2)e ^(jω) ¹ ² , . . . h        _(m)(N−1)e ^(jω) ^(m() ^(N−1))        w _(m)(n)=e ^(jω) ^(m) ^((N−1)/2)(h _(m)(0)e ^(−jω) ^(m)        ^((N−1)/2) ,h _(m)(1)e ^(ω) ^(m) ^((1−(N−1)/) ²⁾ ,h _(m)(2)e        ^(jω) ^(m) ^((2−(N−1)/2)) , . . . , h _(m)(N−1)e ^(jω) ^(m)        ^((N−1)/2))        Since the constant phase does not effect the filtering of the        signal, we can remove it. For ease of notation, we continue to        use the same variable with the constant phase removed.        w _(m)(n)=(h _(m)(0)e ^(−jω) ^(m) ^((N−1)/2) ,h _(m)(1)e ^(jω)        ^(m() ^(1−N−1)/2)) ,h _(m)(2)e ^(jω) ^(m() ^(2−(N−1)/2)) , . . .        h _(m)(N−1 )e ^(jω) ^(m) ^((N−1)/2))        The real part of the m^(th) set of weights is        Re(w _(m)(n))=(h _(m)(0)cos(−w _(m)(N−1)/2),h _(m)(1)cos(−w        _(m)((N−1)/2)−1), . . . , h _(m)(N−2)cos(w _(m)((N−1)/2)−1),h        _(m)(N−1)cos(w _(m)(N−1)/2)        The imaginary part of the mth set of weights is        Im(w _(m)(n))=(h _(m)(0)sin(−w _(m)(N−1)/2),h _(m)(1)sin(−w        _(m)((N−1)/2)−1), . . . ,h _(m)(N−2)sin(w _(m)((N−1)/2)−1),h        _(m)(N−1)sin(w _(m)(N−1)/2)        Note that the real part of w_(m)(n) is symmetric since        corresponding taps are h_(m)(p)cos(−w_(m)((N−1)/2−p)) and        h_(m)(N−1−p)cos(w_(m)((N−1)/2−p)), h_(m)(n) is symmetric        (baseband filter), and cos(−u)=cos(u). Note that the imaginary        part of w_(m)(n) is anti-symmetric since corresponding taps are        h_(m)(p)sin(−w_(m)((N−1)/2−p)) and        h_(m)(N−1−p)sin(w_(m)((N−1)/2−p)) and sin(−u)=−sin(u).        The sum of all of the weights, g(n), shares all of the symmetry        properties of its component filter weights since they are all        the same size and addition does not change symmetry properties        if all of the terms have the same symmetry property. Thus,        g _(c)(n)=Re(g(n))=g _(c)(0),g _(c)(1),g _(c)(N−2),g _(c)(N−1)        where g_(c)(p)=g_(c)(N−1−p)        g _(s)(n)=Im(g(n))=g _(s)(0),g _(s)(1), . . . ,g _(s)(N−2),g        _(s)(N−1)        where g_(s)(p)=−g_(s)(N−1−p)        By using the usual technique of presuming for symmetric filters,        we find that the output can be written as        ${X_{o}(n)} = {{{x_{i}(n)} \star {g(n)}} = {\sum\limits_{k = 0}^{N - 1}{{X_{i}\left( {n - k} \right)}{g(k)}}}}$        ${X_{o}(n)} = {{\sum\limits_{k = 0}^{N - 1}{{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}{{Re}\left( {g(k)} \right)}}} - {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}{{Im}\left( {g(k)} \right)}} + {j\text{(}{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}{{Im}\left( {g(k)} \right)}} + {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}{{Re}\left( {g(k)} \right)}\text{)}}}$        ${X_{o}(n)} = {{\sum\limits_{k = 0}^{N - 1}{{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}{g_{c}(k)}\text{)}}} - {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}{g_{s}(k)}} + {j\text{(}{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}{g_{s}(k)}} + {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}{g_{c}(k)}\text{)}}}$        ${{For}\quad{even}\quad N},{{X_{o}(n)} = {{\sum\limits_{k = 0}^{N - {2/2}}{\left( {{{Re}\left( {X_{i}\left( {n - k} \right)} \right)} + {{Re}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{c}(k)}}} - {\left( {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)} - {{Im}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{s}(k)}} + {{j\left( {{{Re}\left( {X_{i}\left( {n - k} \right)} \right)} + {{Re}\left( {x_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right)}{g_{s}(k)}} + {{Im}\left( {X_{i}\left( {n - k} \right)} \right)} - {{{Im}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}\text{)}{g_{c}(k)}\text{)}}}}$        Grouping the terms alone leads to        ${X_{o}(n)} = {{\sum\limits_{k = 0}^{{({N - 2})}/2}{\text{(}{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}}} + {{{Re}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}\text{)}{g_{c}(k)}} - {\sum\limits_{k = 0}^{{({N - 2})}/2}{\left( {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)} - {{Im}\left( {X_{i}\left( {n - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{s}(k)}}} + {j\left\{ {{\sum\limits_{k = 0}^{{({N - 2})}/2}{\left( {{{Re}\left( {X_{i}\left( {n - k} \right)} \right)} + {{Re}\left( {x_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{s}(k)}}} + {\sum\limits_{k = 0}^{{({N - 2})}/2}{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}} - {{{Im}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}\text{)}{g_{c}(k)}\text{)}}} \right\}}}$        Thus, the implementation is to presume the symmetric taps at the        adders as shown in FIG. 13 thus saving multipliers. The taps        which will be multiplied by the imaginary weights are subtracted        while the taps multiplied by the real weights are added. FIG. 13        is a conceptual drawing showing a symmetric and asymmetric FIR        filter implementation where presuming is performed followed by        multiplication by a coefficient followed by a summing of all of        the products. In actual implementation, each coefficient        multiply occurs at the same time and the outputs are all added.        This is the same as in any FIR filter implementation.        Note that symmetry is exploited, reducing the number of        multiplications required by a factor of one-half.        For odd N, grouping the terms and properly dealing with the        center taps leads to        ${X_{o}(n)} = {\left\{ {{\sum\limits_{k = 0}^{{({N - 3})}/2}{\text{(}{{Re}\left( {X_{i}\left( {n - k} \right)} \right)}}} + {{{Re}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}\text{)}{g_{c}(k)}}} \right\} + {{{Re}\left( {X_{i}\left( {n - {\left( {N - 1} \right)/2}} \right)} \right)}{g_{c}\left( {\left( {N - 1} \right)/2} \right)}} - \left\lbrack {\left\{ {\sum\limits_{k = 0}^{{({N - 3})}/2}{\left( {{{Im}\left( {X_{i}\left( {n - k} \right)} \right)} - {{Im}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{s}(k)}}} \right\} + {{{Im}\left( {X_{i}\left( {n - {\left( {N - 1} \right)/2}} \right)} \right)}{g_{s}\left( {\left( {N - 1} \right)/2} \right\rbrack}} + {j\left\lbrack {\left\{ {\sum\limits_{k = 0}^{{({N - 3})}/2}{\left( {{{Re}\left( {X_{i}\left( {n - k} \right)} \right)} + {{Re}\left( {x_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}} \right){g_{s}(k)}}} \right\} + {j\text{(}{{Re}\left( {X_{i}\left( {n - {\left( {N - 1} \right)/2}} \right)} \right)}{g_{s}\left( {\left( {N - 1} \right)/2} \right)}} + \left\{ {{\sum\limits_{k = 0}^{{({N - 3})}/2}{{Im}\left( {X_{i}\left( {n - k} \right)} \right)}} - {{{Im}\left( {X_{i}\left( {N - 1 - \left( {n - k} \right)} \right)} \right)}\text{)}{g_{c}(k)}\text{)}}} \right\} - {{{Im}\left( {X_{i}\left( {n - {\left( {N - 1} \right)/2}} \right)} \right)}{g_{c}\left( {\left( {N - 1} \right)/2} \right)}\text{)}}} \right\rbrack}} \right.}$        FIG. 14 shows this implementation. Again this is a conceptual        drawing showing a symmetric FIR filter implementation where        presuming is performed followed by multiplication by a        coefficient followed by a summing of all of the products. In the        case of odd length filter coefficients, the center tap is not        pre-summed and is instead simply directly multiplied by its        coefficient.

FIG. 13 is an illustrative implementation of a single Multi bands andArbitrary Shape Filter that support multiple bandpass signals for evenlength filter.

FIG. 14 is an illustrative implementation of a single Multi bands andArbitrary Shape Filter that support multiple bandpass signals for oddlength filter.

Thus, the present invention has been described herein with reference toa particular embodiment for a particular application. Those havingordinary skill in the art and access to the present teachings willrecognize additional modifications applications and embodiments withinthe scope thereof.

It is therefore intended by the appended claims to cover any and allsuch applications, modifications and embodiments within the scope of thepresent invention.

Accordingly,

1. A crest reduction system comprising: first means for suppressing peakamplitudes of an input signal and providing a peak amplitude suppressedsignal in response thereto and second means coupled to said first meansfor rejecting intermodulation distortion in said amplitude suppressedsignal.
 2. The invention of claim 1 wherein said first means is a peakamplitude suppressor.
 3. The invention of claim 2 wherein said peakamplitude suppressor includes means for computing an amplitude of saidinput signal.
 4. The invention of claim 3 wherein said peak amplitudesuppressor includes means for computing a gain factor responsive to saidmeans for computing an amplitude.
 5. The invention of claim 4 whereinsaid means for computing a gain factor includes a lookup table.
 6. Theinvention of claim 4 wherein said peak amplitude suppressor includesmeans for applying said gain factor to said input signal.
 7. Theinvention of claim 1 wherein said means for rejecting intermodulationdistortion includes a plurality of bandpass filters and means forcombining the outputs thereof.
 8. The invention of claim 7 wherein saidmeans for combining is a summer.
 9. The invention of claim 1 whereinsaid means for rejecting intermodulation distortion includes a pluralityof finite impulse response filters.
 10. The invention of claim 9 whereinsaid means for rejecting intermodulation distortion includes a resampleradapted to selectively couple said input signal to said plurality offinite impulse response filters.
 11. The invention of claim 9 whereinsaid means for rejecting intermodulation distortion includes means forperforming a Fast Fourier Transform on outputs of said finite impulseresponse filters.
 12. The invention of claim 11 further including meanscoupled to said means for performing a Fast Fourier Transform forselecting predetermined bands of outputs thereof.
 13. The invention ofclaim 12 further including means for combining outputs of said means forselecting predetermined bands.
 14. The invention of claim 13 furtherincluding means for adding an output of said resampler to an output ofsaid means for combining.
 15. The invention of claim 14 furtherincluding means for delaying said output of said resampler.
 16. A crestreduction system comprising: first means for suppressing peak amplitudesof an input signal and providing a peak amplitude suppressed signal inresponse thereto, said first means including a peak amplitudesuppressor, said peak amplitude suppressor including means for computingan amplitude of an input signal, means for computing a gain factor forsaid input signal in response to said means for computing an amplitude,and means for applying said gain factor to said input signal and secondmeans coupled to said first means for rejecting intermodulationdistortion in said amplitude suppressed signal, said second meansincluding a plurality of bandpass filters and means for combining theoutputs thereof.
 17. The invention of claim 16 wherein said means forcomputing a gain factor includes a lookup table.
 18. A crest reductionmethod including the steps of: suppressing peak amplitudes of an inputsignal and providing a peak amplitude suppressed signal in responsethereto and rejecting intermodulation distortion in said amplitudesuppressed signal.
 19. The invention of claim 18 further including thestep of computing an amplitude of said input signal and computing a gainfactor in response thereto.
 20. The invention of claim 19 wherein saidstep of computing a gain factor includes a step of using a lookup tableto compute said gain factor.
 21. The invention of claim 20 furtherincluding the step of applying said gain factor to said input signal.22. The invention of claim 18 further including the step of filteringsaid amplitude suppressed signal with a plurality of bandpass filters.23. The invention of claim 22 further including the step of selectivelycombining the outputs of said bandpass filters.